Convergence Analysis of Newton-Raphson Method in Feasible Power-Flow for DC Network

Abstract

The Newton-Raphson (NR) method is a powerful tool in nonlinear equations. However, a well-known disadvantage of this method is that the initial iteration value must be chosen sufficiently close to a true solution in order to guarantee its convergence. The Kantorovich theorem is virtually the only known sufficiency condition for convergence of NR method, and gives very conservative bounds. This letter analyzes the convergence of the NR method in feasible power-flow for direct-current (DC) network, and an explicit convergence condition is obtained. Comparing with the existing results, the proposed convergence condition is more concise and less conservative. Moreover, according to the proposed condition, one can easily set the initial iteration value to guarantee the convergence of the NR method. Case studies verify the correctness of the presented analysis.